Full Summary

We can understand an utterance as expressing conceptual content via it playing a role in a particular inferential game of making claims / giving and asking for reasons. For example, that “It’s red” and “It’s green” are incompatible is a move in this game. Other moves include “It’s red” both entailing “It’s colored” and following from “It’s scarlet”. We want to understand the structure of this inferential game.

Formalism is the view that understands “inference” only as “formally-valid inference”. Given some formalization, the example inferences above are conceivable as being formally-valid, but this computer-like approach does not cohere with how humans use learn concepts in practice nor how concepts evolve over time. We are in a much better starting position by being inferentialists who understand inference as “material inference” - i.e. inferences which are “simply good” rather than good due to their logical form. Another reason to prefer this is that we can easily understand the logical inferences in terms of material ones, but not vice-versa: the logical inference is one where we cannot turn it into a materially bad inference via substituting other content for the variables.

A material inference depends on the conceptual contents of the terms which appear in it, yet at the same time, the conceptual contents of something like copper are determined by which (good) material inferences it appears in. By understanding semantics (conceptual content) from pragmatics (practical abilities to master the use of an expression), we do not need spooky metaphysics to understand “grasp of a concept” (e.g. as the turning on of a Cartesian lightbulb).

One way to break this conceptual content down into finer structure is to talk about the introduction and elimination rules for the concept, corresponding to:

Gentzen-style ruleIntroduction rulesElimination rules
Relation to usagethe circumstances under which it’s correctly applied / uttered / usedthe consequences of its application / utterance / use
Pragmaticssufficient conditions for using itnecessary consequences of using it
Consequence of ignoringClassical American pragmatists thought of conceptual content only in terms of consequencesVerificationists consider grasping the circumstances of a concept as grasping the concept
Example of ignoringI can understand the circumstances of something being immoral without having full grasp of the general circumstances for something being immoral“I forsee that I will write a book about Hegel” vs “I will write a book about Hegel” - same circumstances, different consequences

Conservativeness is a technical term which means by introducing a new concept you do not alter the meanings of any statements that don’t involve . Unlike for logical vocabulary, nonlogical concepts are not conservative. The demand that they all be conservative is the demand that we have formal definitions for them all in some logical language, that our inferences are monotonic, that Socratic reflection would never influence us to change our definitions.

Logical vocabulary being conservative explains why it is uniquely suited for helping us talk about material inference. can make explicit the inference from to without modifying their contents. Sellars regarded modal claims as expressing inference licenses (perhaps  expresses the license to express  if one is entitled to , even in the future). This can be likened to common law: intended both to codify prior practice (precedent) expressing explicitly as a rule what was implicit therein, and to have regulative authority for subsequent practice.

Logical vocabulary is very important, but not in the way formalists thought it to be. It allows us to talk explicitly about our inferences (and therefore conceptual contents) in a way that exposes them to critique, so that we can reform or abandon bad concepts.